Solve for $x$ : $x^2 - 7x - 8 = 0$
Explanation: The coefficient on the $x$ term is $-7$ and the constant term is $-8$ , so we need to find two numbers that add up to $-7$ and multiply to $-8$ The two numbers $-8$ and $1$ satisfy both conditions: $ {-8} + {1} = {-7} $ $ {-8} \times {1} = {-8} $ $(x {-8}) (x + {1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x + 1) = 0$ $x - 8 = 0$ or $x + 1 = 0$ Thus, $x = 8$ and $x = -1$ are the solutions.